PQRS is a parallelogram whose diagonals meet at O. A line through O intersects PQ at A and RS at B.Show that ar(ΔAOP)= ar(ΔBOR)
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given that ,
PQ // RS
- when we join AB through O we get AB as a transversal on PQ // RS
- diagonal PR is also a transversal
now , in Δ AOP &ΔBOR
∠ PAO = ∠OBR ( alt. interior angles )
∠AOP = ∠BOR ( v. opp. angles )
∠ APO = ∠ORB ( alt. interior angles )
by AAA Δ AOP is congruent to ΔBOR
⇒ ar. ΔAOP = ar. ΔBOR ( c.p.c.t )
( proved ) ......
PQ // RS
- when we join AB through O we get AB as a transversal on PQ // RS
- diagonal PR is also a transversal
now , in Δ AOP &ΔBOR
∠ PAO = ∠OBR ( alt. interior angles )
∠AOP = ∠BOR ( v. opp. angles )
∠ APO = ∠ORB ( alt. interior angles )
by AAA Δ AOP is congruent to ΔBOR
⇒ ar. ΔAOP = ar. ΔBOR ( c.p.c.t )
( proved ) ......
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in MS paint and there i draw my figure by ruler , curve lines and other shapes and i attach to my answer thats easy
yeah understood
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answer that ABCD Rhombus question
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